To prove they are perpendicular to each other just find the gradients of each side and two of the lines will have gradient m whilst the other two sides will have gradient -1/m

The gradient can be found using (y2 - y1)/(x2 - x1)

So the gradient from (-3,1) to (-1,4) is => (4-1)/(-1-1) = -3/2And the gradient from (-3,1) to (0,-1) is => (-1-1)/(0--3) = 2/3

So just do this for the other two sides, proving their lengths are root 13, and their gradients are m, -1/m, m and -1/m.

(b) is similar. Work out the equations of the diagonals using y = mx + c, filling in the values of y and x for each pair of diagnol coordinates. Then show that the gradient, m, for one diagonal is perpendicular to the other diagnol with gradient -1/m.

(c) is just working out the length of the diagonals using the formulae i gave you in part (a). Simple enough. The values of these lines should come out as √26 since this is what pythagorus theorem suggests.